共查询到20条相似文献,搜索用时 671 毫秒
1.
V.N. Berestovski? 《Differential Geometry and its Applications》2011,29(4):533-546
The authors give a short survey of previous results on generalized normal homogeneous (δ-homogeneous, in other terms) Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with nonnegative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable generalized normal homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds Sp(l)/U(1)⋅Sp(l−1)=CP2l−1, l?2, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval (1/16,1/4). This implies very unusual geometric properties of the adjoint representation of Sp(l), l?2. Some unsolved questions are suggested. 相似文献
2.
We prove that every locally connected quotient G/H of a locally compact, connected, first countable topological group G by
a compact subgroup H admits a G-invariant inner metric with curvature bounded below. Every locally compact homogeneous space
of curvature bounded below is isometric to such a space. These metric spaces generalize the notion of Riemannian homogeneous
space to infinite dimensional groups and quotients which are never (even infinite dimensional) manifolds. We study the geometry
of these spaces, in particular of non-negatively curved homogeneous spaces.
Dedicated to the memory of A. D. Alexandrov 相似文献
3.
Brett Milburn 《Differential Geometry and its Applications》2011,29(5):615-641
The aim of this paper is to study generalized complex geometry (Hitchin, 2002) [6] and Dirac geometry (Courant, 1990) [3], (Courant and Weinstein, 1988) [4] on homogeneous spaces. We offer a characterization of equivariant Dirac structures on homogeneous spaces, which is then used to construct new examples of generalized complex structures. We consider Riemannian symmetric spaces, quotients of compact groups by closed connected subgroups of maximal rank, and nilpotent orbits in sln(R). For each of these cases, we completely classify equivariant Dirac structures. Additionally, we consider equivariant Dirac structures on semisimple orbits in a semisimple Lie algebra. Here equivariant Dirac structures can be described in terms of root systems or by certain data involving parabolic subalgebras. 相似文献
4.
Atallah Affane 《Comptes Rendus Mathematique》2010,348(21-22):1197-1201
We extend to an almost Dirac structure and affine connections the notion of compatibility of a bivectors field or a 2-differential form with a pseudo-metric. Compatibility with a symmetric connection implies integrability. We shall be interested especially by such structures on Lie groups or Riemannian homogeneous spaces. 相似文献
5.
Riemannian supergeometry 总被引:1,自引:0,他引:1
O. Goertsches 《Mathematische Zeitschrift》2008,260(3):557-593
Motivated by Zirnbauer in J Math Phys 37(10):4986–5018 (1996), we develop a theory of Riemannian supermanifolds up to a definition
of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian
and the Lie theoretical viewpoint are introduced, e.g., geodesics, isometry groups and invariant metrics on Lie supergroups
and homogeneous superspaces.
Research supported by the DFG, SFB TR/12 “Symmetries and Universality in Mesoscopic Systems”. 相似文献
6.
The structure of nearly K?hler manifolds was studied by Gray in several articles, mainly in Gray (Math Ann 223:233?C248, 1976). More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a complete strict nearly K?hler manifold is locally a Riemannian product of homogeneous nearly K?hler spaces, twistor spaces over quaternionic K?hler manifolds and six-dimensional (6D) nearly K?hler manifolds, where the homogeneous nearly K?hler factors are also 3-symmetric spaces. In the present article, we show some further properties relative to the structure of nearly K?hler manifolds and, using the lists of 3-symmetric spaces given by Wolf and Gray, we display the exhaustive list of irreducible simply connected homogeneous strict nearly K?hler manifolds. For such manifolds, we give details relative to the intrinsic torsion and the Riemannian curvature. 相似文献
7.
V. V. Gorbatsevich 《Siberian Mathematical Journal》2001,42(6):1036-1046
We consider the isometry groups of Riemannian solvmanifolds and also study a wider class of homogeneous aspheric Riemannian spaces. We clarify the topological structure of these spaces (Theorem 1). We demonstrate that each Riemannian space with a maximally symmetric metric admits an almost simply transitive action of a Lie group with triangular radical (Theorem 2). We apply this result to studying the isometry groups of solvmanifolds and, in particular, solvable Lie groups with some invariant Riemannian metric. 相似文献
8.
Hölder continuity of harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature 总被引:1,自引:1,他引:0
Bent Fuglede 《Calculus of Variations and Partial Differential Equations》2003,16(4):375-403
This is an addendum to the recent Cambridge Tract “Harmonic maps between Riemannian polyhedra”, by J. Eells and the present
author. H?lder continuity of locally energy minimizing maps from an admissible Riemannian polyhedron X to a complete geodesic space Y is established here in two cases: (1) Y is simply connected and has curvature (in the sense of A.D. Alexandrov), or (2) Y is locally compact and has curvature , say, and is contained in a convex ball in Y satisfying bi-point uniqueness and of radius (best possible). With Y a Riemannian polyhedron, and in case (2), this was established in the book mentioned above, though with H?lder continuity taken in a weaker, pointwise
sense. For X a Riemannian manifold the stated results are due to N.J. Korevaar and R.M. Schoen, resp. T. Serbinowski.
Received: 10 October 2001 / Accepted: 20 November 2001 / Published online: 6 August 2002 相似文献
9.
We study Duflo's conjecture on the isomorphism between
the center of the algebra of invariant differential
operators on a homogeneous space and the center of the
associated Poisson algebra. For a rather wide class of
Riemannian homogeneous spaces, which includes the class
of (weakly) commutative spaces, we prove the "weakened
version" of this conjecture. Namely, we prove that
some localizations of the corresponding centers are
isomorphic. For Riemannian homogeneous spaces of the
form X = (H ⋌ N)/H, where N is a
Heisenberg group, we prove Duflo's conjecture in its
original form, i.e., without any localization. 相似文献
10.
A Riemannian g.o. manifold is a homogeneous Riemannian manifold (M,g) on which every geodesic is an orbit of a one-parameter group of isometries. It is known that every simply connected Riemannian g.o. manifold of dimension ?5 is naturally reductive. In dimension 6 there are simply connected Riemannian g.o. manifolds which are in no way naturally reductive, and their full classification is known (including compact examples). In dimension 7, just one new example has been known up to now (namely, a Riemannian nilmanifold constructed by C. Gordon). In the present paper we describe compact irreducible 7-dimensional Riemannian g.o. manifolds (together with their “noncompact duals”) which are in no way naturally reductive. 相似文献
11.
Homogeneous spaces of all compact Lie groups admit Riemannian metrics with completely integrable geodesic flows by means of C
–smooth integrals [9, 10]. The purpose of this paper is to give some constructions of complete involutive algebras of analytic functions, polynomial in velocities, on the (co)tangent bundles of homogeneous spaces of compact Lie groups. This allows us to obtain new integrable Riemannian and sub-Riemannian geodesic flows on various homogeneous spaces, such as Stiefel manifolds, flag manifolds and orbits of the adjoint actions of compact Lie groups.
Mathematics Subject Classification (2000): 70H06, 37J35, 53D17, 53D25 相似文献
12.
《中国科学 数学(英文版)》2015,(7)
In this paper, we find some new homogeneous manifolds G/H admitting non-Riemannian EinsteinRanders metrics when G is the compact simple Lie group E6, or E7 or E8. In the beginning, we prove that these homogeneous manifolds admit Riemannian Einstein metrics. Based on these metrics, we obtain non-Riemannian Einstein Randers metrics on them. 相似文献
13.
A theorem of I. M. Singer [9] states that a Riemannian manifold is locally homogeneous if and only if the Riemannian curvature tensor and its covariant derivatives are the same at each point up to some orderk
M + 1.In the present paper we reprove this theorem by a more direct approach.By using the same approach we also prove, in addition, that a homogeneous Riemannian manifold is completely determined by the curvature and its covariant derivatives at some point up to orderk
M + 2. Moreover, we show how to reconstruct a homogeneous Riemannian manifold only from these curvature data. Finally, we formulate precisely and prove a statement which was announced without proof by Singer in [9].This work was partially supported by the M. P. I. fondi 40%. 相似文献
14.
We continue the study of the δ-homogeneous Riemannian manifolds defined in a more general case by V. N. Berestovski? and C. P. Plaut. Each of these manifolds has nonnegative sectional curvature. We prove in particular that every naturally reductive compact homogeneous Riemannian manifold of positive Euler characteristic is δ-homogeneous. 相似文献
15.
Four-dimensional locally homogeneous Riemannian manifolds are either locally symmetric or locally isometric to Riemannian Lie groups. We determine how and to what extent this result holds in the Lorentzian case. 相似文献
16.
Locally homogeneous Riemannian spaces were studied in [1–4]. Locally conformally homogeneous Riemannian spaces were considered in [10]. Moreover, the theorem claiming that every such space is either conformally flat or conformally equivalent to a locally homogeneous Riemannian space was proved.In this article, we study locally conformally homogeneous pseudo-Riemannian spaces and prove a theorem on their structure. Using three-dimensional Lie groups and the six-dimensional Heisenberg group [11], we construct some examples showing the difference between the Riemannian and pseudo-Riemannian cases for such spaces. 相似文献
17.
18.
Valentino Magnani 《manuscripta mathematica》2003,110(1):55-76
We obtain an intrinsic Blow-up Theorem for regular hypersurfaces on graded nilpotent groups. This procedure allows us to
represent explicitly the Riemannian surface measure in terms of the spherical Hausdorff measure with respect to an intrinsic
distance of the group, namely homogeneous distance. We apply this result to get a version of the Riemannian coarea forumula
on sub-Riemannian groups, that can be expressed in terms of arbitrary homogeneous distances. We introduce the natural class
of horizontal isometries in sub-Riemannian groups, giving examples of rotational invariant homogeneous distances and rotational
groups, where the coarea formula takes a simpler form. By means of the same Blow-up Theorem we obtain an optimal estimate
for the Hausdorff dimension of the characteristic set relative to C
1,1
hypersurfaces in 2-step groups and we prove that it has finite Q–2 Hausdorff measure, where Q is the homogeneous dimension of the group.
Received: 6 February 2002
Mathematics Subject Classification (2000): 28A75 (22E25) 相似文献
19.
20.
The aim of this paper is to study three- and four-dimensional Einstein-like Riemannian manifolds which are Ricci-curvature homogeneous, that is, have constant Ricci eigenvalues. In the three-dimensional case, we present the complete classification of these spaces while, in the four-dimensional case, this classification is obtained in the special case where the manifold is locally homogeneous. We also present explicit examples of four-dimensional locally homogeneous Riemannian manifolds whose Ricci tensor is cyclic-parallel (that is, are of type A) and has distinct eigenvalues. These examples are invalidating an expectation stated by F. Podestá and A. Spiro, and illustrating a striking contrast with the three-dimensional case (where this situation cannot occur). Finally, we also investigate the relation between three- and four-dimensional Einstein-like manifolds of type A and D'Atri spaces, that is, Riemannian manifolds whose geodesic symmetries are volume-preserving (up to sign). 相似文献